In power distribution engineering, power flow analysis is commonly used to obtain the voltage magnitude and the phase angle for each bus in a distribution system, for specified source and load conditions. After the voltages and phase angles are known, currents and powers in each branch, as well as the output of the sources, can be determined analytically. Due to the nonlinear nature of the problem, numerical methods are frequently used to obtain an acceptable solution.
As a special case of power distribution systems, the loads and impedances of a balanced distribution system are three phase balanced, and therefore its steady state performances are usually analyzed by using single-phase power flow analysis with positive sequence parameters.
Depending on known parameters, distribution system buses can be classified as three types:
1. in a swing bus, the voltage magnitude V and the phase angle θ are known;
2. in a PQ bus, the active power P and the reactive power Q are known; and
3. in a PV bus, the active power P and voltage magnitude V are known.
The bus type is determined by the known parameters of connected sources and loads.
Various methods for solving the power flow problem are known. Those methods differ in either the form of the equation describing the system, or the numerical techniques used. A bus admittance matrix based method is widely used. Typical methods include the Gauss-Seidel method, the Newton-Raphson method, and the Fast Decoupled method. Those methods formulate the power flow problems as linear systems and solved the problem by either direct or iterative techniques.